The Nevo--Santos--Wilson spheres are shellable

Nevo, Santos, and Wilson constructed $2^{\Omega(N^d)}$ combinatorially distinct simplicial $(2d-1)$-spheres with $N$ vertices. We prove that all spheres produced by one of their methods are shellable. Combining this with prior results of Kalai, Lee, and Benedetti and Ziegler, we conclude that for all $D \ge 3$, there are $2^{\Theta(N^{\lceil D/2 \rceil})}$ shellable simplicial $D$-spheres with $N$ vertices.